pages/executive-summary/page.md

# Executive summary


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All six registered claims match arXiv v1 and are supported. The complete v1 source contains six concrete algorithm labels, Proposition 1, Theorems 1--2, the CIFAR-10 PGD figures/discussion, and Lemma 1's half-bridge derivation. The current revision is separately pinned because it materially changes the registered `epsilon_opt` exponents.

The deterministic executable now adds 18 continuous non-Gaussian WGF flow cells,
six actual ULA work cells on nonquadratic potentials, and four continuous
half-bridge quadrature cells to the pinned proof checks. All new scope gates
pass: maximum WGF `W1/epsilon` is `0.8185202`, all ULA states are finite with
the largest counted work `1,082,368`, and the continuous KL-decomposition
residual is `5.5511e-17`. The earlier exact source/rate controls and three
primary vector figures remain preserved without fabricating curve coordinates.

Primary records: [OpenReview](https://openreview.net/forum?id=QRtzkKrbJi), [arXiv](https://arxiv.org/abs/2510.25956), [authors' code](https://github.com/ZusenXu/GFS-DRO), and the scheduled [Space](https://huggingface.co/spaces/ProCreations/repro-gradient-flow-sampler-based-distributionally-robust-optimization).

## Scope

| Item | Result |
| --- | --- |
| Exact live claims | 6/6 |
| Scientific gates | 18/18 |
| Literal source | arXiv v1 |
| Current source | Material theory-drift control |
| CIFAR evidence | Pinned primary vector plots and exact source conclusion |
| Independent execution | Non-Gaussian WGF, ULA work, continuous half bridge |


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````html
<iframe src='../../poster_embed.html' style='width:100%;height:400px;border:0' title='Gradient-flow DRO audit poster'></iframe>
````